Estimates in quadratic formulas
It is shown that the problem of estimating quadratic forms can be considered as a problem of computing Gauss and Gauss-Radau quadratures and this problem can be solved using the Lanczos method. Also, the effect of rounding errors to the Gauss quadrature calculations for the distribution function with finite points of increase is analyzed and it is proved that the total error of the Gauss quadrature computed via the conjugate gradient method in finite precision arithmetic can be described as truncation error of the Gauss quadrature for a different distribution function. As a consequence, it is shown that for the particular case \(f(\lambda)= 1/\lambda\), the total accuracy of the Gauss quadrature, computed by the finite precision conjugate gradient process, is determinated by the energy norm of the error of the conjugate gradient process.
scientific article; zbMATH DE number 720553
scientific article